"But this plot takes a backseat to the novel's key concerns: the state of Russian society and the nature of literature as opposed to life. (...) The New Moscow Philosophy's weakness is its lack of vivid characters. It is not a good sign that a list of dramatis personae included at the beginning of the novel is necessary, especially at points in the narrative where there is a clear attempt to increase the suspense among characters." - Stephan Delbos, The Prague Post

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What is most striking about The New Moscow Philosophy is that, despite its title, it offers not so much a novel vision but rather reinforces an established one: this is a story that in large part feels timeless, and could be set (with only the most minor variations) in the Russia of almost any time over the past hundred and fifty years.
In part this is due to how the book is rooted in Dostoevsky's Crime and Punishment, a text (and an influence) that it parodies, but many of its other elements also reinforce that.
The New Moscow Philosophy is set in the waning years of the Soviet Union; published in 1989, its characters already acknowledge: "The times are such that democracy and glasnost decide everything".
The setting and circumstances, however, could be from any Soviet novel from decades earlier, as the action centers around the repeatedly sub-divided Apartment 12 in a "great building at the corner of Petroverigsky Lane", where a variety of tenants uncomfortably share what was once a grand private domicile.
It now houses several different families and individuals, and they all complain about having too little room.
One of the tenants is Alexandra Sergeyevna Pumpianskaya, an old woman, and her sudden disappearance ("into thin air") drives the plot -- with possible motives that might have driven some to a desperate act all too obvious:

The lot of them can hardly wait for her room to be vacated, and for the sake of that little room they're capable of saying anything.
They'd bury Pumpianskaya alive if given half a chance.

The action, which takes place over four days, from a Friday to Monday, follows both their concerns and attempts to find out what became of the old lady and their maneuvering for the room; the mundanely domestic -- everyday life in the crowded apartment -- also contrasts with more ethereal concerns, including a good deal of serious (amateur) philosophizing.
The odd circumstances surrounding Pumpianskaya's death also allows for a variety of speculation that includes the metaphysical -- after all: "There's no evidence of a crime, not even of an incident" (which, of course, turns The New Moscow Philosophy into a sort of anti-Crime and Punishment (since the crime and incident in that story was very real from the start)).
Pyetsukh also firmly roots the novel in the literary: there are those constant echoes of Crime and Punishment, as well as as references -- direct and indirect -- to other Russian and Soviet literature and history (with endnotes helping readers to understand some of these).
And just as Crime and Punishment is, in many respects, timeless, so to The New Moscow Philosophy tries to be similarly universal.
Early on Pyetsukh suggests:

What's important is something else: namely, that in all probability literature is the root of life, so to speak, if not life itself, only slightly displaced along the x-axis, and consequently it should come as no surprise that in Russia where life goes literature follows, but also that where literature goes life follows, that Russians not only write what they live but in part live what they write, that literature has such spiritual authority here

This, surely, is the 'Moscow philosophy' that Pyetsukh means to demonstrate with his story -- and he pulls it off quite well.
Steeped in literature, The New Moscow Philosophy seems in all ways typically Russian (still with a strong Soviet slant), from its possible-murder mystery -- light-hearted but melancholy -- to the heavy layers of inescapable past that all the characters must deal with.
It is a household tale yet includes extensive philosophical exposition, a mix of the everyday and the eternal with, in both cases, a distinctly Russian flair.
Amusing and even touching, The New Moscow Philosophy does feel slightly dated in a post-Soviet world; still, it's more than a relic, and one can both admire and enjoy its cleverness.